Lecture 01 - Coin Tossing.ipynb

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                  "New data (n=100): [1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2]\n",
                  "Last data points: ... [1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2]\n"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "48dmT-b06Qs8"
      },
      "source": [
        "# Throwing a coin or a die\n",
        "\n",
        "Below are some simulations for one of the lab exercises. Sometimes, we can't easily find an answer to a probability  problem using theory. This notebook shows how we can find some answers using simulation instead.\n",
        "\n",
        "First, we need to import some libraries."
      ]
    },
    {
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      "metadata": {
        "id": "cXCsLonp6Qs_"
      },
      "source": [
        "import numpy as np  # Math\n",
        "import random       # Randomness\n",
        "import matplotlib.pylab as plt  # Plotting\n",
        "import ipywidgets as widgets    # Interactive stuff"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z6qgUpj96QtG"
      },
      "source": [
        "The following widget shows the outcome of throwing one (or more) coins or dice. The simulation assumes there is a set number of outcomes (```n_outcomes```) and that all outcomes are equally likely (i.e. a fair die)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HPyuTdq0sVcZ"
      },
      "source": [
        "n_outcomes = 2"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Yr_Fwx7KmRr"
      },
      "source": [
        "Now, when we have defined the number of equally like outcomes, we can run the simulation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lWxtzfdn6hJ_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 498,
          "referenced_widgets": [
            "39796219cce946459ee1c93049a8c4a7",
            "1c93c4ba06a2439ab5ec7186df05ae57",
            "5abdd0e74bc34af487ad66be8759cb3c",
            "03e61611f90a4221a17a6bb814ef4394",
            "43413eb40fd645079915880126a9686f",
            "f44279ed710b4d1397651575c1263509",
            "52a143bef42b456eb8a83c74f092dedc",
            "a971e0af81ae4ecdacd6c1596a83263a",
            "4e9913d32064424f84622f7e99090755",
            "419f7187f60f48ad9bd7af99382f9a67"
          ]
        },
        "outputId": "3e57cf54-c77b-4895-b71d-628d2ef75fb0"
      },
      "source": [
        "data = list()\n",
        "outcomes = list(range(1, n_outcomes+1))\n",
        "print(\"Possible outcomes:\", outcomes)\n",
        "\n",
        "def throw_dice(n_throws):\n",
        "  # Throw the die/coin\n",
        "  new_data = random.choices(outcomes, k=n_throws)\n",
        "  data.extend(new_data)#interact_plot\n",
        "  print(\"New data (n=%i): %s\" % (len(new_data), new_data))\n",
        "  if len(data) < 50:\n",
        "    print(\"All datapoints:\", data)\n",
        "  else:\n",
        "    print(\"Last data points: ...\", data[-50:])\n",
        "  # Define the figures\n",
        "  fig = plt.figure(figsize=(15, 4), dpi=100)\n",
        "  ax = fig.subplots(1, 2)\n",
        "  ax[0].set_ylabel(\"# throws\")\n",
        "  ax[0].set_xlabel('Outcomes')\n",
        "  ax[1].set_xlabel(\"# throws\")\n",
        "  ax[1].set_ylabel('Probability')\n",
        "  # Plot data\n",
        "  data_counts = np.zeros(n_outcomes)\n",
        "  new_data_counts = np.zeros(n_outcomes)\n",
        "  x = np.arange(1, len(data)+1)\n",
        "  for i, outcome in enumerate(outcomes):\n",
        "    data_counts[i] = np.sum(np.asarray(data)==outcome)\n",
        "    new_data_counts[i] = np.sum(np.asarray(new_data)==outcome)\n",
        "    ax[1].plot(x, np.cumsum(np.asarray(data)==outcome)/x,\n",
        "               alpha=.8, label=\"Prob. of outcome %i\" % outcome)\n",
        "  ax[1].plot(x, np.ones(x.shape)/n_outcomes, 'g--', alpha=.8, label=\"Theoretical prob.\")\n",
        "  if n_outcomes == 2:\n",
        "    labels = ['Heads', 'Tails']\n",
        "  else:\n",
        "    labels = [\"Side %i\" % (i+1) for i in range(n_outcomes)]\n",
        "  colours = [\"C%i\" % i for i in range(n_outcomes)]\n",
        "  old_data_counts = data_counts-new_data_counts\n",
        "  ax[0].bar(labels, new_data_counts, bottom=old_data_counts, align='center', color=colours, alpha=.5)\n",
        "  ax[0].bar(labels, old_data_counts, align='center', color=colours, alpha=.8)\n",
        "  # Adjust graphs and commit to screen\n",
        "  a = list(ax[0].axis())\n",
        "  a[3] = max(a[3], 25)\n",
        "  ax[0].axis(tuple(a))\n",
        "  ax[1].legend(loc='upper right')\n",
        "  plt.show()\n",
        "\n",
        "widgets.interact_manual.opts['manual_name'] = 'Throw dice!'\n",
        "interact_plot = widgets.interact_manual(throw_dice, n_throws=widgets.IntSlider(min=1, max=100, step=1, value=1));\n",
        "output = interact_plot.widget.children[-1] # This should prevent flickering\n",
        "output.layout.height = '400px'"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Possible outcomes: [1, 2]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(IntSlider(value=1, description='n_throws', min=1), Button(description='Throw dice!', sty…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "39796219cce946459ee1c93049a8c4a7"
            }
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lh9I0M2AKF33"
      },
      "source": [
        "With two outcomes, why does the orange curve 'inversely' follow the blue curve? Can you see the effect of the *law of large numbers*?"
      ]
    }
  ]
}